Fowler would like to see his old Kop team-mate in the Anfield dugout in the future, but not until current manager Jurgen Klopp has had a long reign at the club.
“You can never say never is football, and Steven is doing a wonderful job up at Rangers," Fowler told talkSPORT. “You've got to ask the question, are they a better team now since he took over? Of course they are, they really are.
“Will he want to leave and go back to the Premier League? No doubt about it and in the future he probably will do.
“He's the name on everybody's lips should Liverpool be looking for a new manager, but as far as I'm concerned I don't want them to be looking for a new manager.
“I want Jurgen to stay for a long time because if he stays for a long time it means Liverpool as a club are successful.
“So all the talk about should Steven be there, of course, he'll be the name on everyone's lips, but I hope it's not for a long time."